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Worked example: Classifying triangles

Work through sample problems categorizing triangles as scalene, isosceles, equilateral, acute, right, or obtuse.  Created by Sal Khan.

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Video transcript

Categorize the following triangles according to whether or not they are obtuse triangles. So an obtuse triangle is a triangle that has an obtuse angle in it, or an angle that is larger than 90 degrees. So it's pretty clear that this one does not have any obtuse angles. This is a 90 degree angle, and these are going to have to be less than 90 degrees. So this is not obtuse. This one right over here, just by looking at it, you see that all of them are less than 90 degrees, so I'll put this not obtuse. Now, these two are interesting. Angle JKL looks like it is larger than 90 degrees, and we can assume that these are drawn to scale, so we can base it on our visual judgment. So I would say that this is obtuse, and angle BAC also looks like it is larger than 90 degrees. So that's an obtuse angle, so I would throw that in the obtuse bucket as well. So we had two not obtuse, two obtuse. Check our answer. Let's do a couple more of these. Which of the following are correct descriptions of triangle PIG? Or I guess triangle pig? Select all that apply. PIG is equilateral. Well, that's not true. To be equilateral, all the sides have to be the same length. And we see here two sides are seven, but one side has length 4. So that's not true. Angle PIG has two equal angles. Well, we see that right over here, these two angles that are 74 degrees. So that's true. Triangle PIG, I guess, has an obtuse angle. Well, an obtuse angle is one that's larger than 90 degrees. None of these are larger than 90. That's not true. Triangle PIG has three acute angles. Well, that is true. All of these angles are less than 90 degrees. Triangle PIG has a right angle. No, none of these angles are exactly 90 degrees, so it does not have a right angle. So let's check our answer. Let's do one more of this. This is actually kind of fun. Categorize the following triangles according to whether or not they are equilateral. So to be equilateral, all of the sides have to have the same length. So this is equilateral. This one, the sides are definitely not the same length. In fact, not even two of the sides are the same length. That's really a scalene triangle. Here we have two sides that are the same length, but the third is different. This would be an isosceles triangle, but it's not equilateral. And here they're all the same length, so we have an equilateral triangle. We got it right.